There is research showing the opposite, though:
Viewers of the BBC’s main news bulletin are likely to have come away with a more favorable impression of Vladimir Putin in the past year than of the European Union.
That’s the extraordinary conclusion drawn by researchers at a Zurich-based media monitoring firm that thinks Britain’s media hasn’t done enough to make the case for the U.K. remaining in the EU.
Coverage of the EU on the BBC’s mainly nightly bulletin, News at Ten, and its flagship current affairs program, Newsnight, was “overwhelmingly negative,” last year, the researchers concluded after reviewing 46,737 news reports on the two shows.
The reports about the EU were so negative, in fact, that Brussels came off worse than the Russian strongman.
Around 45 percent of the BBC’s news coverage of the EU was negative in tone, compared to 30 percent of the coverage of Putin, Media Tenor International said.
The findings don’t necessarily suggest any conscious editorial bias by the BBC against the EU, the researchers said. The complaint (which also applies to popular news programs in other countries) is more that by reporting on Brussels through the lens of national politics — for example, by giving prominence to statements made by the main Westminster party leaders — U.K. viewers are left with a warped and excessively negative view of the EU, which Media Tenor worries could color their decisions in the June 23 referendum.
I haven't read the study and don't know anything about this firm. They could be wrong for all I know. But the point is that the BBC is in a though spot, because it's a hugely divisive topic and no matter what it does it will be accused of bias by someone.